Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.circuits.output_consolidation
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
3	instantiation	92	⊢
	: , :
4	reference	85	⊢
5	reference	50	⊢
6	instantiation	92	⊢
	: , :
7	instantiation	21, 22	⊢
	: , :
8	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
9	instantiation	28, 23, 24, 25	⊢
	: , : , : , :
10	instantiation	51, 26	⊢
	: , :
11	instantiation	92	⊢
	: , :
12	instantiation	51, 27	⊢
	: , :
13	instantiation	28, 29, 30, 31	⊢
	: , : , : , :
14	instantiation	57, 82, 106, 43	⊢
	: , : , :
15	reference	46	⊢
16	reference	79	⊢
17	reference	32	⊢
18	instantiation	56, 32, 33	⊢
	: , :
19	instantiation	34, 75, 35, 36, 37, 38	⊢
	: , :
20	reference	43	⊢
21	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
22	instantiation	39, 85	⊢
	:
23	instantiation	40	⊢
	: , : , :
24	instantiation	53	⊢
	:
25	instantiation	51, 41	⊢
	: , :
26	instantiation	42, 45, 43	⊢
	: , : , :
27	instantiation	44, 45, 46	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	47	⊢
	: , :
30	instantiation	53	⊢
	:
31	instantiation	51, 48	⊢
	: , :
32	instantiation	117, 49, 85	⊢
	: , : , :
33	instantiation	117, 49, 50	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
35	instantiation	88	⊢
	: , : , :
36	instantiation	53	⊢
	:
37	instantiation	51, 52	⊢
	: , :
38	instantiation	53	⊢
	:
39	theorem		⊢
	proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3
41	instantiation	58, 54, 55	⊢
	: , : , :
42	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
43	instantiation	61, 106	⊢
	:
44	theorem		⊢
	proveit.core_expr_types.tuples.partition_back
45	instantiation	56, 116, 77	⊢
	: , :
46	instantiation	57, 106, 104, 95	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2
48	instantiation	58, 59, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
50	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
51	theorem		⊢
	proveit.logic.equality.equals_reversal
52	instantiation	61, 62	⊢
	:
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	instantiation	66, 63	⊢
	: , : , :
55	instantiation	93, 64, 65	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
57	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
58	theorem		⊢
	proveit.logic.equality.sub_right_side_into
59	instantiation	66, 67	⊢
	: , : , :
60	instantiation	93, 68, 69	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.elim_zero_left
62	instantiation	117, 108, 70	⊢
	: , : , :
63	instantiation	74, 75, 71, 116, 77, 119	⊢
	: , :
64	instantiation	102, 101	⊢
	: , : , :
65	instantiation	78, 79, 116, 119, 80, 72, 104, 82, 106, 73*	⊢
	: , : , : , : , : , :
66	theorem		⊢
	proveit.core_expr_types.tuples.range_len
67	instantiation	74, 75, 76, 119, 77	⊢
	: , :
68	instantiation	102, 101	⊢
	: , : , :
69	instantiation	78, 79, 116, 119, 80, 81, 106, 82, 83*	⊢
	: , : , : , : , : , :
70	instantiation	89, 84, 85	⊢
	: , : , :
71	instantiation	88	⊢
	: , : , :
72	instantiation	92	⊢
	: , :
73	instantiation	93, 86, 87	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.addition.add_nat_closure
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
76	instantiation	88	⊢
	: , : , :
77	instantiation	89, 90, 91	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.association
79	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
80	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
81	instantiation	92	⊢
	: , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
83	instantiation	93, 94, 95	⊢
	: , : , :
84	instantiation	98, 96	⊢
	: , :
85	assumption		⊢
86	instantiation	102, 97	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
88	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
89	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
90	instantiation	98, 99	⊢
	: , :
91	instantiation	100, 101	⊢
	: , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
93	axiom		⊢
	proveit.logic.equality.equals_transitivity
94	instantiation	102, 103	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
97	instantiation	105, 104	⊢
	:
98	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
99	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
100	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
101	theorem		⊢
	proveit.numbers.negation.negated_zero
102	axiom		⊢
	proveit.logic.equality.substitution
103	instantiation	105, 106	⊢
	:
104	instantiation	117, 108, 107	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.addition.elim_zero_right
106	instantiation	117, 108, 109	⊢
	: , : , :
107	instantiation	117, 111, 110	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
109	instantiation	117, 111, 112	⊢
	: , : , :
110	instantiation	117, 114, 113	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
112	instantiation	117, 114, 115	⊢
	: , : , :
113	instantiation	117, 118, 116	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
115	instantiation	117, 118, 119	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
117	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements